This paper discusses a design methodology of cooperative trajectory generation for multi-robot systems. The trajectory of achieving cooperative tasks, i.e., with temporal constraints, is constructed hy a nonlinear trajectory generation (NTG) algorithm. Three scenarios of multi-robot tasking are proposed at the cooperative task planning framework. The NTG algorithm is, then, used to generate rea...

We study the concept of quadratic variation a continuous path along sequence partitions and its dependence with respect to choice partition sequence. introduce roughness show that for Hölder-continuous paths satisfying this condition, balanced is invariant Typical Brownian motion are shown satisfy property almost-surely any required step size condition. Using these results we derive formulation...

In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Banaś and L. Olszowy, a...

This paper develops some aspects of stochastic calculus via regularization to Banach valued processes. An original concept of χ-quadratic variation is introduced, where χ is a subspace of the dual of a tensor product B ⊗ B where B is the values space of some process X process. Particular interest is devoted to the case when B is the space of real continuous functions defined on [−τ, 0], τ > 0. ...

This article examines the relationships between interaction (product) terms and curvilinear (quadratic) terms in regression models in which the independent variables are correlated. The author uses 2 substantive examples to demonstrate the following outcomes: (a) If the appropriate quadratic terms are not added to the estimated model, then the observed interaction may indicate a synergistic (of...

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

In this article, we present the least values α1 , α2 , and the greatest values β1 , β2 such that the double inequalities α1L(a,b)+(1−α1)Q(a,b) < M(a,b) < β1L(a,b)+(1−β1)Q(a,b) α2L(a,b)+(1−α2)C(a,b) < M(a,b) < β2L(a,b)+(1−β2)C(a,b) hold for all a,b > 0 with a = b , where L(a,b) , M(a,b) , Q(a,b) and C(a,b) are respectively the logarithmic, Neuman-Sándor, quadratic and contra-harmonic means of a ...

We present a branch and cut algorithm that yields in nite time, a globally -optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. The idea is to estimate all quadratic terms by successive linearizations within a branching tree using Reformulation-Linearization Techniques (RLT). To do so, four classes of linearizat...

Let Fq be a finite field with q elements and let X be a set of matrices over Fq. The main results of this paper are explicit expressions for the number of pairs (A,B) of matrices in X such that A has rank r, B has rank s, and A + B has rank k in the cases that (i) X is the set of alternating matrices over Fq and (ii) X is the set of symmetric matrices over Fq for odd q. Our motivation to study ...